# Conservation of energy - the elevator question

1. Jun 9, 2006

### jamesm113

The cable of a 3750 lb elevator in the figure below snaps when the elevator is at rest at the first floor so that the bottom is a distance d = 12.0 ft above a cushioning spring whose force constant is k = 10,000 lb/ft. A safety device clamps the guide rails, removing 1000 ft-lb of mechanical energy for each 1.00 ft that the elevator moves.

(a) Find the speed of the elevator just before it hits the spring. mgh-1000h=mv^2/2 - 3750(12)-1000(12) = (3750/32)v^/2

v= 23.7318

(b) Find the distance that the spring is compressed. I got 2.8587 ft for this, but apparently it's wrong. Here's what I did:

mv^2/2 + mgx - 1000x = 1/2kx^2
(3750/32)(23.7318^2)/2 + 3750x - 1000x = 10000x^2/2
33000 + 2750x = 5000x^2
x= 2.8587

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2. Jun 9, 2006

### Hootenanny

Staff Emeritus
Perhaps, you forgot to multiply by 'g'?

3. Jun 9, 2006

### jamesm113

3750 lbs. = mg, right?

4. Jun 9, 2006

### Staff: Mentor

Your answers (and method) look OK to me. What makes you think it's wrong?

5. Jun 9, 2006

### jamesm113

I use webassign, a web based homework system and I entered the answer and it said I was wrong.

6. Jun 9, 2006

### Staff: Mentor

Often those systems are picky about the number of significant figures. Does it tell you why your answer is wrong?

7. Jun 9, 2006

### jamesm113

no, and this one gives an error margin of 1%. i've never had sig fig problems before.

8. Jun 10, 2006

### Hootenanny

Staff Emeritus
Ahh yes, I forgot your in pounds. Being a Brit, I'm used to working in kilos and rarely have to deal with lbs. As Doc Al says, I can't see anything wrong with your method. Does webassign allow your to enter exact solutions? In which case the exact solution would be;

$$x = \frac{1}{40}\left( 11 + \sqrt{10681} \right)\; m$$

9. Jun 10, 2006

### Saketh

If you didn't make a significant figures mistake, then the only problem could be an incorrectly entered solution by the instructor. Perhaps he accidentally entered the negative root from the quadratic function instead of the positive root. I am convinced that it is not your mistake.